Infinite precision intermediate arithmetic: how much would break? (opens in new tab)

I wonder how much stuff would break if the rules for evaluating arithmetic expressions were changed like so: All arithmetic expressions are evaluated as-if in ℝ (or ℂ if necessary). In particular, all widening conversions become redundant, and / and >> produce the mathematically correct dividend. At each point where the result of an arithmetic evaluation must be ascribed a definite type, that type is chosen based on surrounding context, and it is an error if the compiler cannot prove that all...